Simplify the following expression: $ p = \dfrac{1}{9} - \dfrac{-8q + 5}{q + 8} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{q + 8}{q + 8}$ $ \dfrac{1}{9} \times \dfrac{q + 8}{q + 8} = \dfrac{q + 8}{9q + 72} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-8q + 5}{q + 8} \times \dfrac{9}{9} = \dfrac{-72q + 45}{9q + 72} $ Therefore $ p = \dfrac{q + 8}{9q + 72} - \dfrac{-72q + 45}{9q + 72} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{q + 8 - (-72q + 45) }{9q + 72} $ Distribute the negative sign: $p = \dfrac{q + 8 + 72q - 45}{9q + 72}$ $p = \dfrac{73q - 37}{9q + 72}$